Assumption: We assume that \(A_m < C_m \forall m\) . It implies that the network is over-confident in its prediction throughout. This is partly true in practice as for all deep neural networks the problem of calibration entails over-confident predictions[1]}. Also, we empirically observed that for networks trained on ImageNet [2]} and CIFAR-100 [3]}, the number of bins for which \(A_m <= C_m\)  holds true are 80 and 95 respectively for \(M=100\) .
